A new adsorption model for describing asphaltene adsorption in dynamic condition at a high temperature and pressure
Tatiana Montoya^{1}, Camilo A. Franco^{2}, Nashaat N. Nassar^{1,*}, Farid B. Cortés2^{}
^{}
^{1}Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada.
^{2}Grupo de Investigación en Yacimientos de Hidrocarburos, Facultad de Minas, Universidad Nacional de Colombia Sede Medellín, Kra 80 No. 65223, Medellín, Colombia, ^{2}Department of
*Corresponding author email: nassar@ucalgary.ca
Abstract
Nowadays, due to the decrease in conventional resources of fossil fuel like light and medium crude oils and to the increase in worldwide energy demand, special attention has been paid to unconventional resources like heavy and extra heavy crude oils, in order to meet the global energy demand. However, heavy and extra heavy crude oils have high viscosities and low API gravities caused by their large content of heavy hydrocarbons, like asphaltenes, affecting the production, transportation and refinery processes. The pressure and temperature are considered as key variables that affect the stability and aggregation behavior of asphaltenes in the reservoir. Normally, asphaltenes are present in crude oil as colloidal suspension surrounded by resins in micelle form[1]. However, many authors[2,3] just have described adsorption isotherms of asphaltenes onto different solid surface at atmospheric pressure without taking into account the aggregation of asphaltenes nor the pressure effect. Therefore, we employed, for the first time, a new model based on the “Chemical Theory”[4] for describing the adsorption behavior of the autoassociative asphaltene molecules at high pressure/temperature onto solid surface. The model is related to the thermodynamic equilibrium of sorption of asphaltenes onto solid surfaces taking into account the imerization of the asphaltenes and its interaction with the surface at different temperatures and pressures. The model is based on the chemical equilibria, equation of state and phase equilibrium. The first two terms describe the behavior of the surface phase, and the phase equilibrium links the surface phase properties to bulk phase properties. These assumptions were used in a previous study to develop the solid–liquid equilibrium (SLE) model to describe the adsorption behavior of asphaltenes onto porous and non–porous solid surfaces. However, the SLE model neglects the effect of pressure on the interactions of asphaltene–asphaltene and asphalteneaggregate–solid surfaces of the reservoir rock primarily at reservoir conditions (RC). Therefore, in this study, a novel and original model called the SLE–RC model of adsorption has been proposed to describe the adsorption mechanism mainly at reservoir conditions, for which the pressure and temperature effect has been evaluated. This model describes the temperaturepressure–dependent adsorption isotherms with five parameters, namely: the maximum amount adsorbed, the constant of the i–mer reactions, Henryxs law constant, the molar volume and the solubility parameter of the asphaltenes. The proposed model has been validated with adsorption tests on porous media under flow conditions at different pressures and temperatures. The dynamic adsorption experiments were performed at different asphaltene concentrations, pressures and temperatures from 100 to 2000 mg/L, 6.89 to 17.24 MPa, and 313 to 353 K, respectively. The SLE–RC model was successfully validated using more than five experimental data describing the adsorption isotherms of the asphaltene onto a packed bed of silica sand at a high pressure and temperature and following a type III behavior with root mean–square errors (RMSE%) below 2%.
Keywords: Adsorption, Asphaltene, High Pressure, Self–Association, SLE–RC model.
The SLERC model
The isotherm equation of the new SLE–RC model that considers the effects of the temperature and pressure is expressed as follows:
_{ }
 (1)

where the definitions of K and ψ are given by:
_{ }
 (2)

_{ }
 (3)

where ξ is a constant defined as ξ =N_{m}/( N_{m}N); N (g/g) is the amount adsorbed, N_{m} (g/g) is the maximum adsorption capacity, K_{T }_{ }is the reaction constant for dimer formation, SA (cm^{2}/g) is the specific surface area of the adsorbent, ν_{as} (cm^{3}/mol) is the asphaltene molar volume, d_{as} (MPa^{1/2}) is the solubility parameter for asphaltenes, and d_{T}_{ } (MPa^{1/2}) is the solubility parameter for the dissolvent.
Figure 1 and Table 1 show some results for test pressures of 6.89, 10.34 and 17.24 MPa and test temperature of 313 K. As shown in Table 1, there is excellent agreement between the SLE–RC model and the experimental results with RMSE% values < 2%. The solubility parameter d_{as} increased as the pressure increased; this is not surprising because the asphaltene solubility is a function of the pressure and is highly dependent on the bubble point of the solvent. The decrease in H indicates that as pressure increases, the number of active sites on the adsorbent would be easily accessible by the asphaltenes, thus increasing the preference of asphaltenes for attaching to the adsorbent surface rather than being present in the bulk phase. Conversely, the increase in K as the pressure increases suggests that the pressure has a significant influence on the self–associative behavior of the asphaltenes on the adsorbent solid surface, indicating that the degree of asphaltene self–association on the adsorbent sites increases as the pressure increases. However, the selfassociation of asphaltenes is strongly dependent on their molecular structure and the interaction that occurs between them and its strength.[58] Additionally, the increasing trend of N_{m} shown as the pressure increases agrees with the experimental results.
Figure 1. Adsorption isotherm of Colombian asphaltenes using a dynamic method
and the results of 5 parameter SLE model for different test pressure and 313 K.
Table 1. Parameters of SLERC model for different test pressures at 313 K.
Parameter
 Test Pressure [9]
 
6.89
 10.34
 17.24
 
H (mg/g)
 8086.42
 7030.61
 3321.65

K (g/g)
 1259.76
 1440.82
 1473.52

N_{m} (g/g)
 0.00668
 0.00708
 0.00879

d_{as} (MPa^{1/2})
 16.56
 16.64
 16.80

ν_{as} (cm^{3}/mol)
 1040.4
 1025.28
 743.74

RMSE%
 1.70
 0.04
 0.63

Conclusion
A new five–parameter SLE–RC model based on “chemical theory” has been introduced for describing asphaltene adsorption at a high temperature and pressure and flow conditions. The model describes well the adsorption isotherms at high pressure/temperature using five parameters found RMS% lower than 10. The proposed new model was used for the first time in this work based on classic thermodynamic concepts to improve the understanding of interactions asphalteneasphaltene and asphaltene–solid surface on the adsorptionequilibrium process at reservoir conditions. This preliminary results based on experimental data of several systems are very encouraging to further pursue the development of the association theory with other solid surfaces as consolidated and other unconsolidated media at reservoir conditions.
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